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For example, in an exchangeable correlation matrix, all pairs of variables are modeled as having the same correlation, so all non-diagonal elements of the matrix are equal to each other. On the other hand, an autoregressive matrix is often used when variables represent a time series, since correlations are likely to be greater when measurements ...
Pearson's correlation coefficient is the covariance of the two variables divided by the product of their standard deviations. The form of the definition involves a "product moment", that is, the mean (the first moment about the origin) of the product of the mean-adjusted random variables; hence the modifier product-moment in the name.
With any number of random variables in excess of 1, the variables can be stacked into a random vector whose i th element is the i th random variable. Then the variances and covariances can be placed in a covariance matrix, in which the (i, j) element is the covariance between the i th random variable and the j th one.
In statistics, spatial autocorrelation between sample locations also helps one estimate mean value uncertainties when sampling a heterogeneous population. The SEQUEST algorithm for analyzing mass spectra makes use of autocorrelation in conjunction with cross-correlation to score the similarity of an observed spectrum to an idealized spectrum ...
If F(r) is the Fisher transformation of r, the sample Spearman rank correlation coefficient, and n is the sample size, then = is a z-score for r, which approximately follows a standard normal distribution under the null hypothesis of statistical independence (ρ = 0). [12] [13]
In statistics, the Kendall rank correlation coefficient, commonly referred to as Kendall's τ coefficient (after the Greek letter τ, tau), is a statistic used to measure the ordinal association between two measured quantities. A τ test is a non-parametric hypothesis test for statistical dependence
In statistics, canonical-correlation analysis (CCA), also called canonical variates analysis, is a way of inferring information from cross-covariance matrices.If we have two vectors X = (X 1, ..., X n) and Y = (Y 1, ..., Y m) of random variables, and there are correlations among the variables, then canonical-correlation analysis will find linear combinations of X and Y that have a maximum ...
In statistics, the coefficient of multiple correlation is a measure of how well a given variable can be predicted using a linear function of a set of other variables. It is the correlation between the variable's values and the best predictions that can be computed linearly from the predictive variables.